Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
int n, a[10000], T[10000];
int main() {
	cin >> n; for (int i = 0; i < n; i++)cin >> a[i];
	sort(a, a + n);
	long double maxn = 0;
	for (int i = 0; i < n; i++) {
		for (int j = i + 1; j < n; j++) {
			T[i] = 1; T[j] = 1;
			vector<int>vec;
			for (int k = n - 1; k >= 0; k--) {
				if (T[k] == 0)vec.push_back(a[k]);
				if (vec.size() == 2)break;
			}
			maxn = max(maxn, 1.0l*(vec[0] + vec[1]) / (a[j] - a[i]));
			T[i] = 0; T[j] = 0;
		}
	}
	printf("%.15Lf\n", maxn);
	return 0;
}